Simplify the following expression: $ x = \dfrac{7}{6} - \dfrac{-5k - 2}{-6k} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-6k}{-6k}$ $ \dfrac{7}{6} \times \dfrac{-6k}{-6k} = \dfrac{-42k}{-36k} $ Multiply the second expression by $\dfrac{6}{6}$ $ \dfrac{-5k - 2}{-6k} \times \dfrac{6}{6} = \dfrac{-30k - 12}{-36k} $ Therefore $ x = \dfrac{-42k}{-36k} - \dfrac{-30k - 12}{-36k} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{-42k - (-30k - 12) }{-36k} $ Distribute the negative sign: $x = \dfrac{-42k + 30k + 12}{-36k}$ $x = \dfrac{-12k + 12}{-36k}$ Simplify the expression by dividing the numerator and denominator by -12: $x = \dfrac{k - 1}{3k}$